# Tagged Questions

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### limsup and liminf of a sequence of points in a set

My ways to define/write limsup and liminf of a sequence of points in a set $X$: They come from what I have understood. If you have other ways of understanding, really appreciate if you can reply ...
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### limsup and liminf of a sequence of subsets of a set

I am confused when reading Wikipedia's article on limsup and liminf of a sequence of subsets of a set $X$. It says there are two different ways to define them, but first gives what is common for ...
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### Proof: Limit superior intersection

How to prove $\limsup(\{A_n \cup B_n\}) = \limsup(\{A_n\}) \cup \limsup(\{B_n\})$? Thanks!
A sequence of sets is defined as $A_n=\{x \in [0,1] : |\sum_{i=0}^{n-1} 1_{[\frac{i}{2n},\frac{2i+1}{4n})} - 1_{[\frac{2i+1}{4n},\frac{i+1}{2n})}| \geq p\}$ for some positive $p\geq0$. What is ...
I am looking for an intuitive explanation of $\liminf$ and $\limsup$ for sequence of sets and how it corresponds to $\liminf$ and $\limsup$ for sets of real numbers. I researched online but cannot ...